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of the value of the advice Felix Klein once gave a perplexed
student who had asked him the secret of mathematical disco-
very. 'You must have a problem', Klein replied. 'Choose one
definite objective and drive ahead toward it. You may never
reach your goal, but you will find something of interest on the
From Deutsch-Krone Weierstrass moved to Braunsberg,
where he taught in the Royal Catholic Gymnasium for six
years, beginning in 1848. The school 'programme' for 1848-9
contains a paper by Weierstrass which must have astonished
the native: Contributions to the Theory of Abelian Integrals. If
this work had chanced to fall under the eyes of any of the pro-
fessional mathematicians of Germany, Weierstrass would have
been made. But, as his Swedish biographer, Mittag-Leffler,
dryly remarks, one does not look for epochal papers on pure
mathematics in secondary-school programmes. Weierstrass
might as well have used his paper to light his pipe.
His next effort fared better. The summer vacation of 1853
(Weierstrass was then thirty-eight) was passed in his father's
house at Westernkotten. Weierstrass spent the vacation writing
up a memoir on Abelian functions. When it was completed he
sent it to Crelle's great Journal. It was accepted and appeared
in volume 47 (1854).
This may have been the paper whose composition was respon-
sible for an amusing incident in Weierstrass' career as a school-
teacher at Braunsberg. Early one morning the director of the
school was startled by a terrific uproar proceeding from the
classroom where Weierstrass was supposed to be holding forth.
On investigation he discovered that Weierstrass had not shown
up. He hurried over to Weierstrass' dwelling, and on knocking
was bidden to enter. There sat Weierstrass pondering by the
glimmering light of a lamp, the curtains of the room still drawn.
He had worked the whole night through and had not noticed
the approach of dawn. The director called his attention to the
fact that it was broad daylight and told hi™ of the uproar in his
classroom. Weierstrass replied that he was on the trail of an
important discovery which would rouse great interest in the
scientific world and he could not possibly interrupt his work,